Gone Home
I think it was my first proper “walking simulator” experience and I remember really enjoying all that I discovered in it. At the time its kind of “explorative narration” felt very interesting to me and still now I think every game that has “narrative” among its perks should be crafted with proper “environmental storytelling”.
Proteus
I found it interesting, while not really my cup of coffee at the time I played it. Exploring for the sake of exploring felt not as fun as I thought, but I may be wrong.
I wonder what will happen if I will play it again.
The Stanley Parable
I only played it recently and personally I found the way it is designed to be amusing.
Putting the humor aside (I never really it was out of place or overdone), I’d say that maybe because it is so “small” in scale, it reminded me how designers can keep almost everything under control while not getting in the way of the players (unless that is the main purpose) and leaving them with a realistic enough sense of freedom.
Virginia
This one I couldn’t appreciate very much. I remember enjoying the whole plot and the overall way the story is presented, but already have vague memories of it even though I played it quite recently.
It was a really slow experience for me and I felt probably too much taken-by-the-hand for my own taste.
Still, I don’t think it is an “objectively” bad game. Certainly there are people who loved it and I can see their point nonetheless 
Two other games off the top of my head, both free and both with no obvious puzzles (the second has none for sure).
Neighbor
By Cardboard Computer, the people who brought us Kentucky Route Zero (that I still have to play completely), comes a pretty much strange adventurous experience set in the desert.
It is included in a collection (which features also work from Tale of Tales and others) made for the Triennale International Exhibition in Milan, originally available on mobile devices (I really like how Neigbhor took advantage of that) and now also available for free on Steam
Packing Up The Rest of Your Stuff on the Last Day at Your Old Apartment
Pretty self-explanatory, this is a short trip in someone’s attempt at packing things up before leaving.
(I remembered that items had no description, but I found out they had)